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Distributive Structure Homology and its Applications to Knot Theory
by
Seung Yeop Yang
George Washington University
Coauthors: J. Scott Carter and Jozef H. Przytycki
The first homology theory using right distributive structures, called rack homology, was introduced by Fenn, Rourke, and Sanderson. Przytycki constructed one-term and multi-term distributive homology theories as generalizations of Fenn, Rourke, and Sanderson's studies. Meanwhile, the rack homology theory was modified to so-called quandle homology by Carter, Jelsovsky, Kamada, Langford, and Saito in order to define cocycle invariants of knots.
We study annihilation of torsion in rack and quandle homology of some finite quandles. Moreover, we discuss applications of distributive structure homology in classical and higher dimensional knot theory.
Date received: December 3, 2016
Copyright © 2016 by the author(s). The author(s) of this work and the organizers of the conference have granted their consent to include this abstract in Topology Atlas. Document # cbnq-38.